**3. Process tomography**

Process tomography gives the opportunity to analyze the processes taking place inside the facility without interfering with the production, analysis, and detection of obstacles, defects, and various anomalies. The tomography belongs to the opposite problems of the electromagnetic field. The inverse problem is the process of identification, optimization, or synthesis, in which the goal is to determine the parameters describing the data [14–16]. Process tomography aims to determine the properties of the tested object from measurements at its edge [17, 18].

Tomography of industrial processes is a harmless, noninvasive imaging technique used in various industrial technologies in processes. It plays an important role in continuous measurement data, which allows better understanding and monitoring of industrial processes, providing a fast and dynamic response, which facilitates process control in real time detecting failures and abnormal system operation. Tomographs allow us to "look inside" pipes in flow reactors. Industrial tomography enables observation of physical and chemical phenomena without the need of internal penetration. In order to obtain information about the test object, measurements are used in various physical phenomena, in which information carriers are X-rays, gamma rays, ultrasounds, electron beams, electric currents, and magnetic fields. The main advantage of tomographic examinations is their noninvasiveness in the

*J* = *E* (2)

A Nondestructive Distributed Sensor System for Imaging in Industrial Tomography

http://dx.doi.org/10.5772/intechopen.79567

31

*E* = −∇*u* (3)

Assuming there are no current sources within the examined region then from Ampère's law:

∇∙ *J* = 0 (4)

∇∙ (*γ* ∇*u*) = 0, (5)

As above the ratio of ωε/σ, when the capacitance or the resistance term is dominant, the

*ω*ε

As a result of the inverse problem solution, the conductivity distribution in the tested area is

A set of electric currents are injected into the examined object through these electrodes, and the obtained voltages are measured using the same electrodes. **Figure 5** shows the opposite method of acquiring boundary potential data illustrated for a cylindrical volumetric guide

In electrical capacitive tomography, the information source is the electrical capacitance between the electrodes located on the perimeter of the measurement sensor (see **Figure 6**). An important feature of the measurement is the non-invasive contact of the sensor with the tested object. Such a solution does not interfere with industrial processes. The advantage of this technique is the quick acquisition of measurement data. The laboratory measuring system

Measurement methods using information contained in the ultrasonic signal after passing through the medium under investigation are called ultrasound transmission methods (see **Figure 8**). Ultrasonic waves belong to short waves and have propagating and radiation properties. The length of these waves depends on the medium to which they are emitted

and 16 equally spaced electrodes: (a) first measurement and (b) second measurement.

*<sup>σ</sup>* ≪ 1 (ERT) (6)

*<sup>σ</sup>* ≫ 1 (ECT) (7)

The potential distribution in the isotropic, inhomogeneous region is as follows:

The gradient of the potential distribution (u) is as follows:

where *u* is the potential.

obtained.

governing equation is further simplified:

with sensors is shown in **Figure 7**.

**4.2. Ultrasound tomography**

∇∙ (*σ* ∇*u*) = 0 *for* \_\_\_

∇∙ (*ε* ∇*u*) = 0 *for* \_\_\_

**Figure 4.** General measurement model for tomography sensors.

studied environment. Such measurements do not change physical and chemical parameters. In the reconstruction of the image, the key parameters are the speed of analysis of flowing raw materials and the accuracy of reconstructed processes. The measurement must be fast because some industrial processes run at high speed. The measuring system consists of a sensor, specialized electronics for capacitance measurement, and data reconstruction and analysis system. Industrial tomography applications are usually a challenge for obtaining spatial distribution data from observations that go beyond the process boundary. The biggest challenge is to achieve effective coverage of closed spaces using practical resources at a reasonable cost. Sensor networks with feedback loops are the basic elements of production control. Distributed infrastructure requires various tasks related to detection and startup and is usually characterized by internal spatial organization. The decisive difference in the mass production of chemicals, food, and other goods is that joint process sensors only provide local measurements. In most production systems, such local measurements are not representative of the entire process; therefore, spatial solutions are necessary. The general measurement model for tomographic sensors is shown in **Figure 4**.
